Primordial black holes and magnetic fields in conformal neutrino mass models

TL;DR

This work analyzes how strongly supercooled first-order phase transitions in conformal $ ext{U(1)'}$ extensions that realize a type-I seesaw for neutrino masses can produce primordial black holes (PBHs) and primordial magnetic fields (PMFs). By RG-improved one-loop potentials and thermodynamic control parameters ($T_p$, $\alpha$, $\beta/H(T_p)$, $T_{\rm RH}$), the authors map PBH abundances and masses across $M_\text{PBH} \in [10^{-18},10^{-9}] M_\odot$ and identify regions yielding SGWB signals detectable by LISA/ET, correlated with Roman microlensing or gamma-ray signals from Hawking evaporation. They also predict magnetic-field strengths $B_\text{peak} \gtrsim 0.5$ pG with coherence lengths $\lambda_\text{peak} \gtrsim 0.008$ Mpc for certain heavy-sector scales, potentially exceeding blazar-derived bounds. The results demonstrate a coherent multi-messenger framework linking dark matter in PBHs, early-universe GW signals, and PMF generation to neutrino mass generation, offering concrete targets for near-future GW detectors, microlensing surveys, and high-energy gamma-ray observatories.

Abstract

Sufficiently strong and long-lasting first-order phase transitions can produce primordial black holes (PBHs) that contribute substantially to the dark matter abundance of the Universe, and can produce large-scale primordial magnetic fields. We study these mechanisms in a generic class of conformal $\mathrm{U(1)}^\prime$ models that also explain active neutrino oscillation data via the type-I seesaw mechanism. We find that phase transitions that occur at seesaw scales between $10^4$ GeV and $10^{11}$ GeV produce gravitational wave signals (from the dynamics of the phase transition and from the decay of cosmic string loops) at LISA/ET that can be correlated with microlensing signals of PBHs at the Roman Space Telescope, while scales near $10^{11}$ GeV can be correlated with Hawking evaporation signals at future gamma-ray telescopes. LISA can probe the entire range of PBH masses between $1\times 10^{-16}M_\odot$ and $8\times 10^{-11}M_\odot$ if PBHs fully account for the dark matter abundance. For Z' masses between 40 TeV and $10^4$ TeV, and 10 TeV right-handed neutrinos, helical magnetic fields can be produced with magnitudes $\gtrsim 0.5$ pG and coherence lengths $\gtrsim 0.008$ Mpc, above current blazar lower bounds.

Figures (9)

• Figure 1: Scatter plots of the PBH abundance, $f_\mathrm{PBH}$, as a function of $M_\mathrm{PBH}$. The color scales indicate the FOPT strength $\alpha$ (top-left panel), its inverse duration $\beta/H(T_p)$ (top-right panel), the percolation temperature $T_p$ (bottom-left), the reheating temperature $T_\mathrm{RH}$ (bottom-right panel). The shaded band enclosed by the black dashed contour is excluded by LVK data ($\mathrm{SNR_{LVK}} > 10$). The green, blue and red dashed contours enclose the regions within the reach of LIGO-O5, ET and LISA with $\mathrm{SNR} > 10$, respectively. The region above the solid black curve is excluded by combination of overabundant PBH production, $\gamma$-ray data and microlensing data. A dedicated microlensing survey of M31 by the Roman Space Telescope is sensitive to the region above the dashed blue curve Drlica-Wagner:2022lbd.
• Figure 2: Top panel: The DM abundance $f_\mathrm{PBH}$ as a function of the critical threshold $\delta_c$ for different values of the inverse time duration $\beta/H(T_p)$ and a fixed reheating temperature $T_\mathrm{RH} = 10^6~\mathrm{GeV}$. Bottom panels: Similar to Fig. \ref{['fig:PHBs_proj_plots_Thermo']}, but the color scale represents the inverse duration $\beta/H(T_p)$ of the FOPT for $\delta_c = 0.4$ (left) and $\delta_c = 0.6$ (right).
• Figure 3: Similar to \ref{['fig:PHBs_proj_plots_Thermo']}, but the color scales represent the $\mathrm{Z^\prime}$ boson mass (top-left panel), the heavy Higgs $h_2$ mass (top-right panel), the largest right-handed neutrino mass (middle-left panel), the Majoron self-interaction coupling $\lambda_\sigma$ (middle-right panel), the gauge coupling $g_L$ (bottom-left panel) and the trace of the Yukawa matrix $\bm{y_\sigma}$ (bottom-right panel).
• Figure 4: Similar to \ref{['fig:PHBs_proj_plots_Thermo']}, but here the color scales represent the SNR at LISA (top-left panel), ET (top-right panel), LIGO O5 (bottom-left panel) and LVK (bottom-right panel). The solid green contours enclose regions with $\mathrm{SNR}>10$.
• Figure 5: Left panel: Parameter space with at least one microlensing event. Right panel: The expected sensitivities of extragalactic $\gamma-$ray signals from Hawking radiation with SNR$>10$ for THESEUS (dotted red curve), GECCO (dashed brown curve), GRAMS (solid green curve), AMEGO$-$X (gray solid curve) and e$-$ASTROGAM (solid orange curve). The color scale in the right panel indicates the predicted SNR for LIGO O5.